Question

The yield to maturity on 1-year zero-coupon bonds is currently 9%; the YTM on 2-year zeros is 10%; the YTM on 3-year zeros is 10.5%. The Treasury plans to issue a 3-year maturity coupon bond, paying coupons once per year with a coupon rate of 11%. The face value of the bond is $1,000.

a) At what price will the bond sell?
b) What will the yield to maturity on the bond be? You can write down the relevant equationinstead if you prefer.
c) If the expectations theory of the yield curve is correct, what is the market expectation of the price that the bond will sell for next year? What is your expected HPR?

Answer 1

The price of a 3-year coupon bond paying an annual coupon rate of 11% will be determined by discounting each of the bond's cash flows back to present value using the given YTM rates. If the coupon rate is above the YTM, the bond will sell at a premium above face value. Market expectations of higher interest rates in the future can lead to a lower price for the bond next year and a higher expected holding period return.

Step-by-step explanation:

Calculating the Bond's Price and Yield to Maturity

To calculate the price at which the bond will sell, we need to discount each of the bond's cash flows back to their present value using the given yield to maturity rates for corresponding maturities. The bond will pay an annual coupon of 11%, which on a face value of $1,000 equates to $110 per year. The cash flows are $110 for the first two years and $1,110 in the third year (which includes the final interest payment plus the face value).

The present value (PV) of these cash flows can be calculated using the formula PV = C/(1+y)^n, where C is the cash flow, y is the yield to maturity (YTM) for the relevant year, and n is the year number.

For a coupon bond with a coupon rate above the market interest rate, we would expect the price to be above the face value. The actual calculation would consider the present value of each of the coupon payments and the face value.

Considering the expectations theory of the yield curve, if interest rates are expected to rise, the bond will sell for less than face value next year because the coupons would be less attractive relative to new bonds with higher rates. The expected holding period return (HPR) would reflect these market expectations and the change in the bond's price.

For example, if interest rates rise and the bond's price falls to $964 while an investor receives an interest payment of $80, then the yield on the bond will be higher than the coupon rate, reflecting the discounting effect of the higher market interest rates.